Conformal Killing horizons and their thermodynamics

Abstract

Certain dynamical black hole solutions can be mapped to static spacetimes by conformal metric transformations. This mapping provides a physical link between the conformal Killing horizon of the dynamical black hole and a Killing horizon of the static spacetime. We show how this conformal relation can be used to derive thermodynamic properties for the dynamical black holes. Although these horizons are defined quasi-locally and can be located by local experiments, they are distinct from other popular notions of quasi-local horizons such as apparent horizons. Thus in the dynamical Vaidya spacetime describing constant accretion of null dust, the conformal Killing horizon, which is null by construction, is the natural horizon to describe the black hole.

5 pages

References in corpus (9)

• The (pseudo)issue of the conformal frame revisited
• Dynamical surface gravity
• The region with trapped surfaces in spherical symmetry, its core, and their boundaries
• Testing General Relativity with Accretion-Flow Imaging of Sgr A*
• Ten Proofs of the Generalized Second Law
• Black holes and black hole thermodynamics without event horizons
• Local Invariants Vanishing on Stationary Horizons: A Diagnostic for Locating Black Holes
• The spatial relation between the event horizon and trapping horizon
• The slicing dependence of non-spherically symmetric quasi-local horizons in Vaidya Spacetimes

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• Shadows of Kerr-Vaidya-like black holes
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• On the existence of conformal Killing horizons in LRS spacetimes
• Bit Threads: From Entanglement to Geometric Entropies
• Gradient conformal stationarity and the CMC condition in LRS spacetimes
• Null infinity as a Killing horizon
• Homothetic Killing horizons in generic Vaidya spacetimes
• What can we learn from the conformal noninvariance of the Klein-Gordon equation?
• Generalized Eddington--Finkelstein Coordinates and Exact Vaidya-Type Solutions in Weyl Conformal Gravity